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L Candelori (2014)
Harmonic weak Maass forms of integral weight: a geometric approachMath. Ann., 360
N Katz (1973)
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RF Coleman, B Edixhoven (1998)
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J Bruinier, K Ono, R Rhoades (2008)
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RF Coleman (1996)
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RF Coleman (1989)
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K Bringmann, P Guerzhoy, B Kane (2012)
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Bringmann et al. (Trans Am Math Soc 364(5):2393–2410, 2012) showed how to ‘regularize’ mock modular forms by a certain linear combination of the Eichler integral of their shadows in order to obtain p-adic modular forms in the sense of Serre. In this paper, we give a new proof of a refined form of their results (for good primes p) by employing the geometric theory of harmonic Maass forms developed by Candelori (Math Ann 360(1–2):489–517, 2014) and the theory of overconvergent modular forms due to Katz and Coleman. In particular, our main results imply that the p-adic modular forms in Bringmann et al. (2012) are overconvergent.
Research in the Mathematical Sciences – Springer Journals
Published: Mar 3, 2017
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